The ex-Serbia international was released after four years with Birmingham at the end of last season, and won League Cup with the club in 2011.
However, the former Valencia man was also part of the side that got relegated to the second tier during the same season, with Zigic believed to have been among the highest earners at St Andrews.
The club suffered financial problems following their relegation and Zigic left the club during the tenure of Lee Clark.
However, Clark's successor Rowett has expressed a desire to see what the free agent could offer.
"Obviously he is a player who is available and I am aware of the contribution to this club over the last four years," he told the Birmingham Mail. "We have had a chat and invited him to come and train with us.
"It's just a mutual thing at present: we can have a look at him, he can have a look at us and how we do things, as we are a new management team."
Rowett also suggested Zigic would likely need to accept reduced terms if he were to return to the club on a permanent basis.
"Nikola is aware of the financial boundaries in place," he added. "But he is keen to stay and play in this country and I am sure this club still means a lot to him."
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